Wireframe modifier with intersection "nodes"
This can be accomplished through instancing.




Create your object
Duplicate the object SHIFT+D
Add a wireframe modifier to the duplicated object
Parent the original object to the duplicated object: Select the original object first, then the duplicate and press CTRL+P, Set Parent to > Object.
Create a sphere object and scale it to the desired size.
Parent the sphere to the original object: Select the sphere first, then the object and press CTRL+P, Set Parent to > Object.
Select the original object and open the Object tab in the properties. In the Instancing panel enable instancing for Verts and disable Render Instancer


The instructions above create instances of the sphere at the vertex positions of the object and a wireframe version of it. The duplicate object is necessary because the wireframe modifier creates new geometry, which would be used by the instancing. This would result in spheres being placed at the vertices of the generated wireframe mesh instead of the original vertex positions.

You can download the example project below: